Which is more efficient - bullet shape or pure teardrop?

Discussion in 'Aircraft Design / Aerodynamics / New Technology' started by Thunderchook, May 29, 2017.

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  1. May 29, 2017 #1

    Thunderchook

    Thunderchook

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    So, what do the wind tunnel tests show?

    Which is more aerodynamically perfect - a standard bull-shaped design (e.g. Winton Facet Opal) or an actual, pure teardrop shape which actually bulges at the front and then tapers towards the back?

    bullet.png teardrop.jpg

    What do the experts say?

    Thanks,

    Thunderchook.
     
  2. May 29, 2017 #2

    Aesquire

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    At subsonic speed, teardrop.

    Supersonic? Pointy teardrop.

    Bullets would be teardrop shape except the problem of stabilizing that shape in the barrel and the gunpowder displaced by the tail.

    Thus bullets are cylinders with rounded or ogive pointy noses. Pointy better supersonic. And cut flat or boat tail shortened compromise tails.

    Hornady installed a new Doppler radar system in their ballistic tunnel. ( indoor underground shooting range to allow year round testing ) and discovered the trajectory on their polymer tipped long range bullets was.... wrong. Turns out the tips were melting and ruining the air flow. They then developed a new heat resistant tip and can extend predictable trajectories out past 800 meters.

    Short answer. Bullets have their shape as a compromise of factors. Some have nothing to do with aerodynamics.. Teardrop are much closer to the ideal...... elliptical far better than circular.
     
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  3. May 29, 2017 #3

    MadRocketScientist

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    I'm no expert but my money is on the teardrop for subsonic speeds and the bullet shape for supersonic ;)

    Shannon.
     
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  4. May 29, 2017 #4

    Aesquire

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    To be more precise, an elliptical teardrop of 3 to 1 or somewhat better length to width ratio.

    The bullet shape is constrained by it's purpose... it has to be propelled down the barrel. And in most cases, spun by the rifling in the barrel. So a bullet needs some bearing surface against the barrel, and the thin band around a teardrop is not generally good enough. Thus the cylinder shape. The length is constrained by the specs on the cartridge, to fit in the magazine and feed through the action. A longer bullet can in many cases be loaded through the ejection port, and this technique is used with precision hand loaded cartridges by some target shooters. However even there, the position of the beginning of the rifling in the barrel can limit how long the bullet can be.

    Generally, bullet makers consider a bullet more like an arrow than a ball to be better at long range. Really high aspect ratio bullets are rare, due to multiple factors, and are limited to some smoothbore hyper velocity tank rounds. ( if you consider a 155 mm dia sabot around a tungsten dart a bullet... )

    If you skip the whole, "has to be shot down a tube by expanding gasses" limitation of rifle bullets, and consider historical projectile weapons, the Military Sling ( spin around David & Goliath type, not Dennis the Menace back pocket Y shape ) in Roman times used massed produced fire hardened clay rounded teardrops. ( often with insults etc. scratched into them before baking "Catch this" and "Yo mamma" were common. In Latin, of course ) Considering a Sling at the time had longer range than a monolithic wooden bow of the era, they had that figured out pretty good.

    Catapult projectiles tended to be spheres for accuracy. ( no matter how they rolled/yawed/pitched they had the same shape to the air ) Accuracy was often surprisingly good.

    The other common projectiles were either spin stabilized, ( arrows ) with fins, or shaft stabilized ( javelins ). Generally these were made at least partly from wood, and needed more "sectional density" than rock to carry much distance.

    Sectional density isn't a term often used in airplanes. Airplanes aren't usually tossed in ballistic arcs. ( some are, and we have stories ) ;)

    Airplanes use "drag" and Drag coefficient, to compare shapes. Teardrops are better than arrows, too... for drag.
     
  5. May 29, 2017 #5

    pictsidhe

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    Subsonic, it's rumoured that a bullet will fly better backwards. As others have said, bullets have to make a lot of compromises and their aerodynamics are far from ideal. The teardrop is the most subsonically aerodynamic known shape.
     
  6. May 29, 2017 #6

    Little Scrapper

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    If I recall, the book "Speed with Economy" explored this. I believe he even made a drawing of the ratios?
     
  7. May 29, 2017 #7

    Xanadrone

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    What about a third variant? - the so-called Goldschmied shape, thought to be somehow... self-propulsive also by the creator of the late (?) Synergy by McGinnis (btw, do you know something new about the fate of his audacious project? -- maybe too audacious, because started directly with a 5/6-seater and some cashflow crisis.)

    @MadRocketScientist: the perfect fuselage form for your Cri-Cri (congrats for the progression!) would be in my opinion... without the canopy. ;) Not with an open-air cockpit though - so that is not entirely a joke, me thinking of a prone-piloted Cri-Cri and even trying to design a similar one (sort of, whilst even smaller and biplane).

    PAV_SAE_Winner_Goldschmied.jpg
     
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  8. May 29, 2017 #8

    Swampyankee

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    Well, first one must define the "best" shape: by volume or by frontal area?

    The bullet shape has a large area of separation at the base; this is a major source of drag.

    Minimal drag is achieved, sub-sonically, when there is no separation and minimal turbulent flow. In trans- and super-sonic conditions, one adds the need to minimize shocks, but doesn't lose the need to minimize turbulent flow and separation. This results in the Sears-Haack body (note that it doesn't have that draggy base).
     
  9. May 29, 2017 #9

    wsimpso1

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    A few points not mentioned (from a guy who did ammo engineering including some bullet aerodynamics work in his first job out of college):

    In addition to bullets having to support compact ammunition, bullets have to stay in shape for handling, feeding through the mechanism, firing and then reliable trajectories as they fly through the air. All of this severely compromises the design. I just did a quick calc of a 30 cal target bullet. Peak force accelerating the bullet is about 4400 pounds, peak acceleration is about 5.8 million ft/s/s or about 180,000 g's. At the point of peak pressure, the bullet has already been freed from the expanding case, been thrust into the tapered leade, engraved into the rifling, had a gas plasma of above 7000 F scorching the back end. Through all of this, it is accelerating to 200,00 rpm and the nose of the bullet can not be allowed to slump over to one side. If the pointed end slumps, rotational imbalance will drive the barrel end into a rotating movement and will cause the bullet to jump laterally as it leaves the now gyrating barrel. Inaccuracy...

    Bullets have to be sturdy so their flight will be predictable. This is more important than low drag. About drag of bullets. A 308 Win throwing a 168 grain match bullet at 2550 feet per second will have slowed to sonic (1050 ft/sec or so) somewhere around 900 yards and takes about 1.6 seconds to do that. Yeah, it decels about 1000 ft/s/s. Even artillery shells in high arc trajectories have slowed to sub-sonic velocities on the descent. Bullets are not terribly good things to emulate for drag.

    One last point, if bullets were not gyroscopically stabilized, they would tumble, but given that they are spun to spectacular rpm, they fly with the nose high and to one side, not straight on, and the error between bullet direction and flight path increases as the flight goes on. At 1000 yards, 190 grain bullets leave a noticibly oblong hole in the paper...

    Stick with airfoil shapes for airfoils. They work better.

    Billski
     
  10. May 29, 2017 #10

    Norman

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    Fuselage shapes are compromises between cargo shape, wing interaction, tail length, engine inlets, and the need to have a thrust producer. The ideal shape for low subsonic flight is a fairly fat teardrop but the tail usually causes it to be stretched out some. Then the engine makes it necessary to chop one end off. Chopping off the pointy end of a teardrop does make it look like a bullet. Modern sailplanes show the best compromise for tail length: a short fat teardrop shaped pod with a boom to hold the tail on but there's not much room for cargo. When you chop one end off to make room for a propeller you create a big flat spot in one of the two worst places. A prop spinner can partially get back to the original shape and can be worth a few knots for either a tractor or a pusher.
     
  11. May 29, 2017 #11

    Jimstix

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    A couple of things, you need to add some qualifiers to your question, such as 1) if both objects have the same frontal area, 2) if both objects are traveling at the same airspeed, and 3) both objects have the same wetted area.
    Go to Hoerner and look up the drag coefficient, Cd as a function of Mach number for each shape and open a new Excel worksheet. You will need four columns, one for Mach number, one for the Cd as a function of Mach number, one for the bullet Cd * area, one for the drop Cd * area.
    Make a chart of the resulting Mach vs Cd*Area calculations. You will get two curves, one for the drag of the bullet and one for the drag of the drop plotted against the Mach number on the x-axis and drag on the y-axis.
    If you start with Mach numbers of 0.1 and increase in even increments of 0.1 up to Mach 1.0 you will see the drag curve of the drop increase much more rapidly than that of the bullet as you get above about Mach 0.3 to 0.5.
    Jim
     
  12. May 29, 2017 #12

    Aerowerx

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    The over all length of a cartridge is fixed for the specific firearm. With a longer bullet the extra length has to go inside the case. Any extra length outside the case, and it would be dangerous to fire, if it even chambers.

    IIRC, the reason precision shooters load each round by hand is for consistency, not because of length. And most of them are bolt action anyway, IIRC. Precision shooters tend to baby everything anyway.

    Supersonic rifle bullets tend to have higher aspect ratios than low speed pistol bullets. There is such a difference between bullet dynamics and airplane dynamics I don't think you can make any legitimate comparisons between them.
     
  13. May 29, 2017 #13

    Aesquire

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    Overall, I agree.

    You can position the bullet out of the front of the case past the spec limit only a little, before it runs into the rifling on the barrel. Some target shooters do so, but they have carefully measured the dimensions and are right up against the physical limits, and even then the cartridge won't "work" in the action, ( feed through as the bolt is moved ) and must be hand fed, carefully, one at a time. Positioning a longer bullet deeper into the case to keep overall length in limits, displaces powder, and reduces the available velocity.

    The ideal is to keep the bullet supersonic all the way to the target. When a bullet falls below supersonic speed, it tends to pick up a wobble... and accuracy goes away. The Sears-Haack body is great once it leaves the barrel, but has serious issues with displacing propellent. ( fuel ) https://en.wikipedia.org/wiki/Sears–Haack_body

    sears-haack-bullet.jpg

    The constraints on body shape are different for planes than bullets. The science for airplanes is, in part, based on the early ballistics research, but no one I know goes back to Galileo for the math to build a wing. ( his math for cannon balls, OTOH was groundbreaking :) Few use it for artillery today, but he started the science )

    As you can see the Sears-Haack shape is not very useful, as a pure shape, for airplane fuselages. For drop tanks, especially on transonic airplanes, sure.

    The flat base on a bullet is a compromise. The shape of a fuselage after body is also a compromise, but to different needs. ( you seldom need your tail to withstand 30,000 psi of fire )

    And as another useless fact about bullets that doesn't apply to a Kitfox..... High speed bullets have traditionally been made of lead ( heaviest/cheapest preindustiral material available ) covered with a copper alloy jacket. The shell is for 2 reasons. The copper alloy doesn't smear as much going through the rifling. Lead alloy bullets just get the outside torn off as they are pushed though the rifling, and foul everything up, quickly, at supersonic speeds. The copper alloy also strengthens the bullet, mostly for terminal ballistic effects, ( outside the scope of this discussion ) but also to withstand the rotational speeds. A thinly jacketed bullet, pushed beyond it's design speeds and rotation, will actually disintegrate into a puff of vaporized metal a few feet past the end of the barrel. I've seen it. At first the shooter was perplexed he was missing the target so badly. They just were not getting that far.

    This may affect how you think about props and turbines, though. ;)

    Modern ballistic calculators have to take into account the Coriolis effect of the Earth's rotation as well as the gyroscopic effects of the bullet actually pointing away from the target. Onboard GPS correction is currently only available at the high end of the cost & size spectrum....

    Like airplanes before hand held Gps Systems. :)

    I wouldn't hold my breath for guided rifle bullets outside Science Fiction. Electronic laser range finding scopes with onboard ballistics computers are now available, and the lidar equipped ones to measure cross winds will eventually find their way down to consumer level gear. ( Tanks have this stuff, at least in experimental versions, today )

    Now THAT technology will relatively soon be available to home builders for airplanes. Lidar to see cross winds and shear will eventually fit into your glass cockpit. Bullet shapes? not so much.
     
  14. May 29, 2017 #14

    cheapracer

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    I am led to believe that "coke bottle" shape is the most aerodynamic?
     
  15. May 29, 2017 #15

    Aesquire

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    I will point out that a LOT of this stuff, bullets, wing airfoils, and fuselage shapes, were approximated by trial and error, without a solid mathematical base to predict changes. Just because it wasn't figured out with Computational Flow Dynamics, doesn't mean it doesn't work.

    However when you get to the tricky bits, like the wing/fuselage junction of a sailplane, and want to optimize it as much as possible, you do go past the Tony Fokker "see the spray" level of aerodynamics I'm used to, and more computing power than that planet had when I was in high school is a must have. ( I never forget my phone is more "powerful" than EVERYTHING NASA had during the Apollo program. )

    The Intel based PC I'm typing this on is a bit slow for CFD calculations today. It's Video card is better at those. Some modern "supercomputers" used in CFD are basically banks of video cards linked together. ( faster processor, faster memory, programmable architecture. )

    Heck, who would have thought 20 years ago that a Cub could have a glass cockpit more capable than a 747's? ( my buddy's planned Eindecker will probably have a Dynon mini thingee )
     
  16. May 29, 2017 #16

    BJC

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    The coke bottle fuselage shape is used to achieve a total airplane cross-section area that increases and then decreases smoothly from nose to tail. See "area rule." It is not necessary for a bullet because a bullet has no wings that affect cross-section area.


    BJC
     
  17. May 29, 2017 #17

    Aesquire

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    That's based on the idea that the cross section of the entire airplane should be a smooth curve, nose to tail. No abrupt rises in cross section = less drag. ( at transonic speed, especially ) Called "Area Ruling".

    The coke bottle shape came when you narrow a cylindrical fuselage to compensate for the cross section of the wings.

    Another example of that is the bulges on the tail of the F-102.

    https://en.wikipedia.org/wiki/Convair_F-102_Delta_Dagger

    note the differences between the YF-102 & the YF-102A. Not just a corset around the waist shape, but bulges at the tail to smooth out the curve.
    edit... ya beat me :)
     
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  18. May 29, 2017 #18

    lr27

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    To really answer a question like this, we have to nail down a lot of things. Some of them have been mentioned, such as whether you're optimizing for cross section or volume. Obviously Mach number and Reynolds number enter into it too. Plus, is the fuselage on a pylon or something so we don't have to worry about interactions with wings, engines, landing gear or other stuff? Also, how smooth you can make the fuselage matters too. If it's free of waves and very smooth, you can sustain laminar flow. Shapes to maximize laminar fly vary greatly depending on the Reynolds number. For turbulent flow, I think something more or less resembling a tear drop shape is optimal, though again the optimal thickness to length will vary by Reynolds number. The higher the Reynolds number, the blunter the shape. With laminar flow, the thickest point, at moderate Reynolds numbers, will be further back. However, for really big stuff it will be considerably further forward, I think. For examples, see the pictures on page 8 and 9 of DRAG REDUCTION AND SHAPE
    OPTIMIZATION OF AIRSHIP BODIES by Th. Lutz and S. Wagnery
    http://tinyurl.com/ybg5nob5
    I expect this sounds dry, but the shapes are pretty interesting, and, as the Reynolds numbers get higher, some are really counter-intuitive. If you were making a 1,000 passenger, slow airliner, and you could solve problems like landing gear and wing attachment, you could have a truly bizarre shape, maybe even like the one in figure 11 or figure 12. But that's a tall order, this side of gravity control. For many homebuilts, figure 9 is probably of the most interest.
     
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  19. May 30, 2017 #19

    Swampyankee

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    No, the coke bottle shape is because the goal is to have the aircraft's overall area distribution match that of a Sears-Haack body; this has to include the wing and empennage.
     
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  20. May 30, 2017 #20

    pictsidhe

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    My favourite example of area rule is the dorsal tank added to the EE lightning.
     

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